Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3798 conjugacy classes of subgroups; only the 824 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 824 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291259 | C2 | direct (N × H) |
| 2. C2×#16811571 | C2 | semidirect |
| 3. C2×#16811568 | C2 | semidirect |
| 7. #16811571 | C22 | semidirect |
| 8. #16811568 | C22 | semidirect |
| 11. C2×#13133214 | C4 | semidirect |
| 12. C2×#13133213 | C4 | semidirect |
| 13. #127×D53 | C4 | semidirect |
| 16. C2×#127×C53 | C4 | semidirect |
| 24. C22×D212 | C2×C4 | semidirect |
| 25. C22×C22⋊D53 | C2×C4 | semidirect |
| 28. C2×D4×D53 | C2×C4 | semidirect |
| 31. #13133214 | C2×C4 | semidirect |
| 32. #13133213 | C2×C4 | semidirect |
| 33. C2×C4×Dic53 | C2×C4 | semidirect |
| 34. C42×D53 | C2×C4 | semidirect |
| 36. C22×D4×C53 | C2×C4 | semidirect |
| 37. #127×C53 | C2×C4 | semidirect |
| 38. C2×C42×C53 | C2×C4 | semidirect |
| 51. C2×D4×C53 | C22×C4 | semidirect |
| 54. C2×C22⋊D53 | C22×C4 | semidirect |
| 60. C2×D212 | C22×C4 | semidirect |
| 65. C42×C53 | C22×C4 | semidirect |
| 66. C4×Dic53 | C22×C4 | semidirect |
| 113. C2×C53 | #2380 | semidirect |
| 116. D53 | #2380 | semidirect |
| 124. C2×#127 | #6157 | semidirect |
| 130. C53 | C2×#2380 | semidirect |
| 138. C22×D4 | C2×#6157 | semidirect |
| 145. #127 | C2×#6157 | semidirect |
| 151. C2×C42 | C2×#6157 | semidirect |
| 168. C2×D4 | C22×#6157 | semidirect |
| 180. C42 | C22×#6157 | semidirect |
| 225. C2 | #20291259 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291259 | 2 |
| C2×#16811571 | 2 |
| C2×#16811568 | 2 |
| C2×#127×D53 | 2 |
| C2×#2380 | 53 |